Condition on the first black draw before counting the remaining whites

A bag initially contains 3 white and 6 black balls. A player draws 3 balls, one at a time, without replacement. Three white balls win the grand prize; exactly two whites win a consolation prize; otherwise the player wins nothing.

Find the probability that

(i) a player wins the grand prize,

(ii) a player wins a consolation prize,

(iii) a player wins a consolation prize, given that the first draw is black.